Interactive comment on “ Method to measure the size-resolved real part of aerosol refractive index ”

The present manuscript describes a method for deriving the real part of the refractive index by means of a differential mobility selector (DMA) and scattering intensities measured with a SP2. The derivation of the real part of the refractive index of a quasi mono disperse aerosol is not completely new. What is new, however, is the application with the use of the SP2, which in a unique way can also determine the mixing state of the aerosol within certain limits. This ensures that errors caused by unknown imaginary parts of the refractive index are minimised. The method shown is limited to non-absorbent particles.


Introduction
Aerosols exert significant influence on the earth energy budget by scattering and absorbing radiation (Ramanathan and Carmichael, 2008).There still remain great uncertainties when estimating the aerosol effective radiative forcing (RF) (Ghan and Schwartz, 2007) and an accurate estimation of the aerosol optical properties can help reduce the RF variations.The optical properties of the ambient aerosol particles are determined by their particle size and complex refractive index (RI, m=n+ki) (Bohren and Huffman, 2007;Levoni et al., 1997).Despite that the ambient aerosol particle size distribution can be measured with high accuracy (Wiedensohler et al., 2012), an accurate measurement of the ambient aerosol RI remains challenging.The RI is also widely used in remote sensing (Redemann et al., 2000;Dubovik, 2002;Zhao et al., 2017) and atmospheric modelling (Ghan and Schwartz, 2007;Kuang et al., 2015) because the aerosol single scattering albedo (SSA) and aerosol scattering phase function are highly related with the RI.At the same time, a small uncertainty in the real part of the RI (RRI) can lead to great uncertainties when estimating the aerosol RF.Zarzana et al. (2014) finds that a variation of 0.003 in RRI can lead to uncertainties of 1% in RF for non-absorbing ammonium sulfate particles.Moise et al. (2015) estimates that the RF will increase 12% when the RRI varies from 1.4 to 1.5.Valenzuela et al. (2018) also reports an uncertainty of 7% with the uncertainties of RRI of 0.1 in RRI.Therefore, it is pressing that the uncertainties of the RI be reduced when estimating the RF.
Many methods were proposed to derive the RRI.The RRI can be estimated by linear volume average of the known aerosol chemical components by where   and   is the volume fraction and known partial refractive index of ith component (Wex et al., 2002;Hand and Kreidenweis, 2002;Hanel, 1968;Liu and Daum, 2008).The aerosol RRI can also be calculated by partial molar refraction approach (Stelson, 1990;Hu et al., 2012) which is essentially consistent with the linear volume method (Liu and Daum, 2008).The ambient aerosol RRI can be derived by synthetically using the radiative transfer calculations and the ground-based solar extinction and scattering measurements (Wendisch andHoyningen-Huene, 1994, 1992).Sorooshian et al. (2008) developed a method to measure the aerosol RRI based on the differential mobility analyzer (DMA) and an optical particle counters.The RRI is retrieved from the known particle size from the DMA and the aerosol scattering intensity from the Optical Particle Counter (OPC) for aerosol particles larger than 500nm.The Scanning Mobility Particle Sizer (SMPS) and OPC is used in combination to derive the RRI by aligning the particle size distributions in the instrument overlap regions (Hand and Kreidenweis, 2002;Vratolis et al., 2018).The aerosol effective RRI is also retrieved by applying Mie scattering theory to the aerosol particle number size distribution, aerosol bulk scattering coefficient and aerosol absorbing coefficient data (Cai et al., 2011;Liu and Daum, 2000).Spindler et al. (2007) retrieved the aerosol RRI value by using the cavity ring-down spectroscopy to measuring the scattering and absorbing properties of bulk aerosols.Eidhammer et al. (2008)) measured the light scattering at different angles and retrieved the RRI.Similarly, the aerosol RRI is retrieved by measuring the aerosol phase function (Barkey et al., 2007).Recently, a method by using the single particle mass spectrometry is proposed to measure the aerosol RRI (Zhang et al., 2015).At the same time, aerosol time-of-flight mass spectrometer is proved to be capable of measuring the aerosol RRI (Moffet et al., 2008).The aerosol RRI can also be retrieved from the Mie spectroscopy by using the optical tweezers in the laboratory (Shepherd et al., 2018).
Up to now, there is no information in the literature of the size-resolved ambient aerosol RRI over the diameter range between 200nm and 500nm where the aerosol scattering coefficients contributes to the total scattering coefficients most (Tao et al., 2017;Kuang et al., 2018).All the instruments expressed as: where Qsh is the sheath flow rate; r1 is the outer radius of annular space and r2 is the inner radius of the annular space.The transfer function refers to the probability that a particle with a certain electrical mobility can pass through the DMA.For a given V, the transfer function is triangular-shaped, with the peaking value of 100% and a half width (HW) of (3).
The aerosol Zp, which is highly related to the aerosols diameter (Dp) and the number of elementary charges on the particle (n), is defined as: where e is the elementary charge; µ is the gas viscosity coefficient, C(Dp) is the Cunningham slip correction that is defined by: where τ is the gas mean free path.
Based on the discussion above, the aerosols that pass through the DMA with the same Zp, can have different Dp and different elementary charges.

SP2
The SP2 is a widely used instrument that can measure the optical properties of every single particle.
The measurement principle and instrumental setup of the SP2 have been discussed in detail previously (Stephens et al., 2003;Schwarz et al., 2006)  Bridging the scattering H values measured by the SP2 scattering channel and the scattering intensity defined by equation 6 is achieved by calibrating the SP2 with ammonium sulfate.The instrument setup of the calibration procedure is the same as that described in section 2.2.1.The diameters of the aerosols passing through the DMA are manually changed from 100 to 450nm with a step of 10nm.For each diameter, the scattering H value and incandescence signal of every particle are analyzed.When calibrating, there is no aerosol whose incandescence signal exceeds 1000, which means that the SP2 works stably and the incandescence signal channel can well distinguish the BC containing aerosols.
After the calibration, the size-resolved RRI can be retrieved with known aerosol diameter selected by DMA and the corresponding aerosol scattering H values measured by SP2.

Multiple Charging
Fig. S2 gives the aerosols scattering H probability distribution under different aerosol diameter.
For each diameter, the distributions of the scattering H may have more than one mode for both the high gain and low gain channels.The following discussions would give explanation about the multiple mode distributions of H.
For each mode, the number of recorded aerosol particles at a given H is fit by the log-normal distribution function: Where   is the geometric standard deviation;  0 is the geometric standard mean H and  0 is the number concentrations for a peak mode.The geometric standard deviation is highly related to the half width of the transfer function (equation 3) and the H0 is discussed below in detail.should increase with the increment of Dp.Thus, the black square markers in fig. 2 represent the aerosols that are singly charged.At the same time, the relationships between the H0 and Dp can be interpolated.
Other colored markers represent that the aerosols have more than one charge.We calculated the corresponding diameter of the aerosols that share the same Zp but different charges at the given Dp by the DMA (Dp � ).Then the corresponding H0 at Dp � are calculated and shown in dashed line in fig. 2.
From fig. 2, the calculated H0 shows good consistence with the measured H0.
From the discussion above, we conclude that the SP2 detect those ammonium sulfate aerosols with the diameter larger than 160nm.However, the ambient aerosol RRI is always lower than that of ammonium sulfate (Liu and Daum, 2008) Fig. 4(a) gives the relationships between the calculated scattering intensity and the SP2 aerosol scattering H at different diameter.When calculating the scattering intensity, the RRI value of ammonium sulfate is set to be 1.521.We can see that the aerosol scattering intensity shows good consistence with the peak height (R 2 =0.9992).
Furthermore, the RRI of the scattering aerosol at a given diameter can be retrieved using the corresponding scattering H. the DMA and SP2 can be used to derived the aerosol RRI with high accuracy.

Validation of the calibration
Fig. S3 gives the corresponding results of the scattering low gain channel.In fig.S3, the relationship between the aerosol scattering peak height of the low gain channel and the scattering strength is determined.At the same time, the comparison between the measured peak height and the calculated peak height shows good consistence too.

Field Measurements
Figure 5 shows the measured average probability distribution of the ambient size-resolved RRI and the measured mean PNSD.From fig. 5, we can see that the derived RRI is 1.46±0.02and doesn't vary significantly with diameter between 199 nm and 436 nm.The measured aerosol PNSD during the measurement has a maximum of 26400 #/cm 3 at 107 nm.Based on the measured PNSD and the measured RRI, the size distribution of the scattering coefficient is calculated based on the Mie scattering theory.The results in fig. 5 show that the measured RRI diameter range covers most of the aerosol that contributes significantly to the aerosol scattering properties.Thus, the derived sizeresolved RRI of this range is representative of the ambient aerosols scattering properties.

Uncertainty analysis
The factors that influence the accuracy of retrieving RRI include the aerosols scattering H measured by SP and the aerosol diameter selected by DMA.
The uncertainties of the selected diameter by DMA is well characterized based on equation 2 and 3.The uncertainties from the DMA transfer function can be avoided by fitting the scattering H using the log-normal distribution function.However, the uncertainties of the measured H from the SP2 remain unknown.The HW of the transfer function is 0.1 times the scanning diameter, which means that the geometric standard deviation of the aerosol PNSD selected by the DMA is estimated to be 1.102.At the same time, the measured geometric standard deviation of the measured H mode by SP2 is 1.182.Thus, the geometric standard deviation of the measured H from the SP2 is estimated to be 1.073, whose corresponding uncertainties is 6.8%.
The uncertainties of the retrieved RRI to the variations in the measured H are analyzed using the Mie scattering theory and the corresponding results are shown in fig.6.The variations in RRI increase with the increment of RRI but decrease with the increment of the Dp.For most ambient aerosols, the Table 1 lists the retrieved ammonium chloride RRI under different diameter.The absolute difference between the retrieved RRI and theoretical values is always smaller than 0.02 regardless of the particle diameter, which means that the measured RRI is in line with the theoretical one.Thus, we conclude that the uncertainty of the retrieved RRI is within 0.02.

Conclusions
Knowledge on the microphysical properties of ambient aerosol is import for better evaluating their radiative forcing.The aerosol RRI is a key factor that determines the aerosol scattering properties.
In this study, a new method to measure the ambient aerosol RRI is developed by synthetically using a DMA in tandem with a SP2.This method can continuously measure the size-resolved RRI over a wide range between 198 nm and 426 nm with an accuracy of 0.02.At the same time, it is free from the influence of the BC containing aerosols.
The basic principle of measuring the size-resolved RRI is to select the aerosols at a certain diameter by the DMA and measure the corresponding scattering intensity by the SP2.The relationship between the aerosols scattering intensity and the peak height of the scattering signal channels are determined by calibrating the SP2 using ammonium sulfate (RRI=1.521).
The method is validated by using the ammonium chloride with the RRI of 1.642 as sample aerosol and the corresponding derived size-resolved RRI is 1.642±0.02.
This instrument is employed at a field measurement at the AERONET PKU stating, the sizeresolved RRI of the ambient aerosols is 1.46 and doesn't show significant variation among the diameter.
The corresponding aerosol diameter range, which can be detected by SP2 to derive the RRI, covers most of the aerosol scattering.Thus, the derived size-resolved RRI of this range can be used as a good representative of the ambient aerosols scattering properties.
and will be briefly described here.When the sample aerosol particles pass through the continuous Nd:YAG laser beam at 1064nm with power about 1 mW/cm 2 , eight sensors distributed at four directions are synchronously detecting the emitted or scattered light by using avalanche photo-detector (APD) at different angles (45 o and 135 o ).For each direction, the two APDs sample the same signal with different sensitivities to get a wider measurement range.The low gain channels are less sensitive to the measured signal and can be used to measure the stronger signal of larger particles.In accordance, the high gain channels are more sensitive to the measured signal, and can be used to measure the weaker signal of smaller particles.The optical head of the SP2 is shown schematically in fig.1(b).In this study, we utilize signals from four channels of the SP2: two of them measure the scattering signals and another two measure the incandescent light between 350 nm and 800 nm.The peak height (H) of the incandescence signals is used to infer whether the sampled aerosol contains the black carbon (BC).If the H of the incandescence signal is larger than 500, the sample aerosol contains the BC and the scattering signals should deviate from the signals of pure scattering aerosol.Those sample aerosols are ruled out when dealing with the aerosol scattering signals.strength measured by the SP2 From fig. 1(b), the APDs of the SP2 receive signals that were scattered by the sampled aerosols from the directions at 45 o and 135 o .Thus, the scattering intensity (S) measured by the APD can be expressed as: S = C • I 0 •  • ( 45  +  135  ) (6), where I0 is the laser's intensity;  is the scattering coefficient of the sampled aerosol,  45  and  135  are scattering phase function at 45 o and 135 o respectively of the sampled aerosols; and C is constant that is determined by the distance from the aerosol to the APD and the area of the APD.The scattering intensity of the aerosol is recorded as the H of the scattering signals by SP2.Therefore, the SP2 can be used as a powerful tool to measure the scattering signals of the sampled aerosol and the Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-399Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 27 November 2018 c Author(s) 2018.CC BY 4.0 License.influence of the BC on the aerosol scattering properties can be avoided.Based on the Mie scattering theory, ,  45  and  135  are determined by the size and RRI of the aerosol.The amount of scattering signals from the sample aerosol varies with the diameter and RRI of the aerosol (Bohren and Huffman, 2007).The scattering intensity at different aerosol diameter and RRI is calculated based on equation (6) and shown in fig. 2. The C is assumed to be 1 here.From fig. 2, we can see that the aerosol scattering intensity increases homogeneously with the increasing aerosol RRI at a given Dp, which makes it possible to retrieve the aerosol RRI when the Dp and the scattering intensity are known.

6
Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-399Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 27 November 2018 c Author(s) 2018.CC BY 4.0 License.The H0 values of each mode at different diameters are labeled with different markers in fig. 2. The   is fitted to be a small range at 1.182±0.02for different mode and different aerosol diameter.In the following discussion, we conclude that the different PH0 values in fig. 3 represent that the aerosols are charged with different number of elementary charges.Based on the Mie scattering theory (Bohren and Huffman, 2007), the scattering intensity increases with increasing Dp, which imply that the H0 , thus the lower detecting limit of the ambient scattering aerosols should be larger than 160nm.The measured H0 of the SP2 scattering low gain channel signals are shown in fig.S2.From fig.S2, the same results can be deduced as those of the high gain channel signals.
Ammonium chloride is used to validate the method of deriving the RRI from SP2.The RRI value of ammonium chloride is 1.642.The scattering H of the ammonium chloride under different diameters are measured and analyzed.Fig. 4(b) shows the comparison between the measured scattering high gain peak height and the theoretical peak height at different aerosols diameter.Results show that the measured peak height and the calculated ones are well correlated with R 2 =0.9994, which means that Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2018-399Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 27 November 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 2 .
Figure 2. The distribution of the aerosols scattering strength at different Dp and different RRI.

Figure 3 .
Figure 3.The geometric mean peak height for different diameters of the high gain.The markers gives 418

Figure 4 .
Figure 4. (a) the relationship between the scattering peak height from the SP2 high gain scattering 422

Figure 6 .
Figure 6.The variation in RRI for different kinds of aerosols that have different diameters and different RRI.